A theater can seat 638 people. the number of rows is 7 less than the number of seats in each row. how many rows of seats are there?

Rows = x

seats per row=x+7

and total seats = rows times seats per row or x (x+7) or x^2+7x=seats = 638

so if you subtract 638 from both sides you can get an equation thatyou can factor out (x^2+7x-638) = 0

638 factors out to 2 times 11 times 29 so

(x-22) (x+29) = 0

so x-22=0

x=22

or x+29=0

x=-29 but you can't have a negative number of rows so this answer is wrong

so the answer is there are 22 rows and 29 seats (22+7=29)

Form an equation using the information given.

x = number of sets in a row

x - 7 = number of rows

x (x - 7) = 638

x^2 - 7x = 638

make a quadratic equation

x^2 - 7x - 638 = 0

then solve either using quadratic equation or find two numbers that add to make - 7 and multiply to make - 638, one number is negative and one is positive, as the product of the numbers is negative.

-29 + 22 = - 7

-29 x 22 = - 639

then put into brackets

(x - 29) (x + 22) = 0

when the equation equals zero you can find two values for x

x = 29 or - 22